A hint of frustration flashed across Israeli Deputy Defense Minister Danny Danon's face when I asked him about the criticism he has received from American Jewish establishment organizations concerning his rejection of the two-state solution.

"If American Jewish organizations will call upon the Israeli prime minister to fire me because of my opinion on the two-state solution, it's crossing the line," Danon told me on his recent visit to New York, referring to recent statements issued by both the Anti-Defamation League and the American Jewish Committee that charged him, as well as his ministerial colleague Naftali Bennett, with damaging Israel's image because of their forthright views.

"I can't imagine that the same Jewish organizations would have called upon [the late Israeli Prime Minister Yitzhak] Shamir to fire Shimon Peres when he was promoting one of his peace plans," Danon added, invoking the uneasy left-right coalition government that ruled Israel for much of the 1980s. "When the government leans to the left, they will support it 'unconditionally.' If the government is positioned to the right, you start to see maneuvering not to support it."

My purpose in relating this conversation is not to trigger yet another debate about the role of American Jewish organizations in dutifully restating the positions of the White House in their dealings with Israeli officials. Danon's comments are instructive because they demonstrate that influential Israelis are reconsidering what has become, for both American Jewish leaders and the American administration, an article of faith: namely, that the two-state solution is the only show in town.

There is an understandable reluctance to question both the wisdom and the viability of a two-state outcome to the Israeli-Palestinian conflict. Traditionally, this has been the preserve of Palestinian extremists, like the Hamas regime in Gaza, who reject Israel's very identity as a Jewish state.

Equally, there is no reason to allow those who would happily annihilate Israel to frame the terms of the discussion. Israel has to make its calculations based upon its own interests. As far as Danon is concerned, Palestinian intransigence has left the case for the two-state solution looking flimsy. As he argued in a recent New York Times op-ed, Israel would be better off annulling the Oslo Accords and seeking a solution to the Palestinian issue that places more responsibility upon Egypt for the Gaza Strip, and more responsibility on Jordan for the West Bank.

Such a stance is radically removed from the official American position, which continues to pursue the two-state solution, most recently through Secretary of State John Kerry's initiative, which has been heavy on PR and light on impact.

It suggests—as the Israeli political analyst Yossi Klein Halevi observed last week in the Wall Street Journal in a piece highlighting Prime Minister Benjamin Netanyahu's pledge that Israel "will not allow Iran to get nuclear weapons"—that on both the Palestinian and Iranian fronts, Israel might decide that a "strained relationship with the White House" is a less risky option.

Of course, no one wants that scenario to become reality—Danon, for one, genuinely believes that there is a special relationship between the U.S. and Israel that needs to be preserved—but at the same time, Israel cannot allow vital security decisions to be determined by whatever ideas happen to be in vogue in Washington. And looking at the Kerry initiative, the holes are painfully visible. Indeed, we talk about a two-state solution as if the very real split between the Fatah-ruled West Bank and Hamas-ruled Gaza were taking place in a parallel universe, rather than being a powerful reason why the two-state solution is looking rather haggard.

During our talk, Danon mentioned the "Iron Wall," a concept that originated with the great Revisionist Zionist leader Ze'ev Jabotinsky who described it, in a 1923 essay, as a "strong power in Palestine that is not amenable to any Arab pressure." Jabotinsky did not argue that an agreement with the Arabs is eternally doomed—his point, which remains valid today, was that a sovereign Jewish state must approach the issue from a position of confident strength.

That doesn't mean just military strength. It also means, I'd venture, alliances with other peoples in the region, like the Kurds, who have suffered from both Arab chauvinism and Islamist extremism. Above all, it means having the courage, as Danny Danon does, to start thinking alternatively.